论文标题
具有均匀误差的结构保存算法，用于高度振荡的哈密顿系统的长期节能
Structure-preserving algorithms with uniform error bound and long-time energy conservation for highly oscillatory Hamiltonian systems
论文作者
论文摘要
结构保存算法和具有均匀误差的算法构成了两种有趣的数值方法。在本文中，我们将这两种用于求解非线性哈密顿系统的方法具有高度振荡的解决方案，混合算法继承并尊重每种方法的优势。提出了两种算法，分别保留了哈密顿系统的符合性和能量。此外，所提出的算法被证明在高度振荡结构中具有统一的误差。通过显示混合算法的性能，进行了数值实验，以支持本文中建立的理论结果。
Structure-preserving algorithms and algorithms with uniform error bound have constituted two interesting classes of numerical methods. In this paper, we blend these two kinds of methods for solving nonlinear Hamiltonian systems with highly oscillatory solution, and the blended algorithms inherit and respect the advantage of each method. Two kinds of algorithms are presented to preserve the symplecticity and energy of the Hamiltonian systems, respectively. Moreover, the proposed algorithms are shown to have uniform error bound for the highly oscillatory structure. A numerical experiment is carried out to support the theoretical results established in this paper by showing the performance of the blended algorithms.
